Consider a 5-year structured product of European type code-named "GOLDEN-GOAL" offered by a multinational investment bank to High-Net-Worth Individuals (HNWIs) that is linked to the Hang Seng Index with the following terms: - Issue Price: USD 1 billion (USD 1,000 million) - Issuance date: 26 June 2023 - Terminal date: 26 June 2028 - Initial Hang Seng Index on 26 June 2023: 19,800 - Payment at terminal date (per USD1,000) is as follows: H2028 and HS2023 are respectively the Hang Seng Index on 26th June 2028 and 26th June 2023. It is believed that the Hang Seng Index will fluctuate with 15.75% volatility each year for the next 5 years. The risk-free interest rate is 7%. Assume that Hang Seng Index doesn't pay dividend. (a) Determine the fair value of "GOLDEN-GOAL". (10 points) (b) Determine the sensitivity of GOLDEN-GOAL price to the volatility of Heng Seng Index by plotting the price of GOLDEN-GOAL against the Hang Seng Index volatility. (10 points) (c) How sensitive is "golden-goal" price to stock market volatility; that is, how much the price will change if volatility varies between 10% and 20% ? (5 points) (d) Is GOLDEN-GOAL a very risky investment? (5 points)